Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many type of solutions?

Please provide the name for each type of solution.

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many type of solutions?

Please provide the name for each type of solution.

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

Type of solution of quadratic depends on the value of Discriminant: b^2 - 4ac

Roots are evaluated by factoring the equation of

aX^2 + bx + c

a ( X - b/ 2a ) ^2 - ( b^2 - 4ac)/ 4a^2

X_{1}_{ }, X_{2 } = -b/2a ±√(b^2 - 4ac) /2a

if b^2 - 4ac > 0 , then quadratic has 2 real roos

a. b^2 -4ac is a perfect square then the roots are rational

b . b^2 - 4ac not a perfect square, then the roots are irrational

if b^2 - 4ac< 0 , then quadratic has 2 complex roots.

Quadratic always has 2 roots.

The irrational and complex roots has to appear as conjugate pair for the coefficients of the quadratic

to be integers.

i.e.

X = a ± bi

X = a ± √b

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